Measures of Central Tendency

Topics Covered in this Session

Measures of Central Tendency

Definition – averages or what is typical for a group of values such as scores, grades, etc. The three major measures of central tendency are the mean, median and mode.
The median is useful when very high or very low numbers may distort or skew a mean. For example, the mean ($110,400.) for the following annual salaries
$ 10000.
$ 12000.
$ 15000.
$ 15000.
$ 500000.
$552000. / 5 = $110400. – Calculation for the Mean
is skewed because of one very high salary ($500000.) and does not accurately indicate what is typical of this group. The median which is $15000. is more typical and a more accurate measure of central tendency in this example. The median is used extensively when presenting data such as salaries, incomes, prices of houses, etc.
Of the above measures of central tendency, the mean is by far the most extensively used in educational research.

T-test

The t-test is a parametric (assumes normal distribution) test to determine the significance of the difference between the mtheans of two groups of values. The t-test uses the mean, the variance and a Table of Critical Values for a “t” Distribution to calculate a t value. The rejection or acceptance of the significance of the differences in two means is based on a standard that no more than 5% of the difference is due to chance or sampling error, and that the same difference would occur 95% of the time should the test be repeated. Some researchers use a more rigorous standard of 1% (.01 Level), and that the same difference would occur 99% of the time should the test be repeated.
The t-test usually is displayed in a study or report as follows: The experiment or treatment group (M=86.50, SD=4.31) scored significantly higher than the control group (M=79.10, SD=5.22), t(80) = 4.90, p<.05 where
In the above example, p is the bottom line value and indicates at what level a statistically significant difference exists.

Analysis of Variance (ANOVA)

Analysis of variance is a statistical measure used for determining whether differences exist among two or more groups. It does this by comparing the means of the groups to see if they are statistically different. Analysis of variance uses the mean, the variance and a Table of Critical Values for “F” Distribution to calculate an F statistic. Analysis of variance is a parametric (assumes normal distribution) test. Statistical significance of the differences in two or more means is based on a standard that no more than 5% (.05 Level) of the difference is due to chance or sampling error, and that the same difference would occur 95% of the time should the test be repeated. Some researchers use a more rigorous standard of 1% (.01 Level), and that the same difference would occur 99% of the time should the test be repeated.
Depending on the options used, ANOVA can be displayed in different ways in a study or a report. For an N-way ANOVA, the following is typical. The analysis of variance indicated that there were significant differences among the four groups F(3, 96)=7.50, p<.01 where

Scheffe Test

The Scheffe test is used with ANOVA (Analysis of Variance) to determine which variable(s) among several independent variables is statistically the most different.

Chi-Square

T-test and analysis of variance are parametric statistical procedures that assume that the distributions are normal or nearly normal and is used when variables are continuous such as test scores and grade point averages. Chi-square is a nonparametric statistical procedure used to determine the significance of the difference between groups when data are nominal and placed in categories such as gender or ethnicity. This procedure compares what is observed against what was expected.

FOR MORE INFORMATION ON THE TOPICS COVERED IN THIS SESSION, PLEASE REFER TO THE APPENDIX IN A.G. PICCIANO "EDUCATIONAL RESEARCH PRIMER" AS WELL AS THE MANUALS AND DOCUMENTATION PROVIDED BY SPSS, INC.